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Unit 1 - Lesson 16 - Grade 8: Illustrative Mathmatics

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16 Questions
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Grade 8 Unit 1
Lesson 16: Parallel Lines and the Angles in a Triangle
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 1
Lesson 16: Parallel Lines and the Angles in a Triangle
CC BY 2021 Illustrative Mathematics®
Lesson: Parallel Lines and the Angles in a Triangle

True or False: Computational Relationships (Warm Up)

Is each equation true or false?
1.

2.

3.

Angle Plus Two

Here is triangle ABC.
4.

Rotate triangle ABC 180° around the midpoint of side AC. Label the new vertex D.

5.

Rotate triangle ABC 180° around the midpoint of side AB. Label the new vertex E.

6.

Look at angles EAB, BAC, and CAD. Without measuring, write what you think is the sum of the measures of these angles. Explain or show your reasoning.


7.

Is the measure of angle EAB equal to the measure of any angle in triangle ABC? If so, which one? If not, how do you know?


8.

Is the measure of angle CAD equal to the measure of any angle in triangle ABC? If so, which one? If not, how do you know?


9.

What is the sum of the measures of angles ABC, BAC, and ACB?

Every Triangle in the World

Here is Δ ABC. Line DE is parallel to line AC.
10.

What is

Explain how you know.


11.

Use your answer to explain why
a + b + c = 180.

12.

Explain why your argument will work for any triangle: that is, explain why the sum of the angle measures in any triangle is 180°.

Four Triangles Revisited (Optional)

This diagram shows a square BDFH that has been made by images of triangle ABC under rigid transformations.
13.

Given that angle BAC measures 53 degrees, find as many other angle measures as you can.


Cool Down: Angle Sizes

Angle Sizes

14.

In an equilateral triangle, all side lengths are equal and all angle measures are equal. Sketch an equilateral triangle. What are the measures of its angles?


15.

In an isosceles triangle, which is not equilateral, two side lengths are equal and two angle measures are equal. Sketch three different isosceles triangles.

16.

List two different possibilities for the angle measures of an isosceles triangle.